Recent works [1]}, [2]}, [3]} aim to understand the relation between the message passing in GNNs and label homophily from the interactions between GNNs (model) and graph topology (data). For graph data with a high label homophily coefficient, existing works [1]}, [5]} have demonstrated, either provably or empirically, that the nodes with higher node degree obtain more prediction benefits in GCN, compared to the benefits that peripheral nodes obtain. As for graph data with a low label homophily coefficient, GNNs does not necessarily lead to better prediction performance compared with MLP since since the node features of neighbors with different labels contaminates the node features during feature aggregation. However, although work [6]} empirically points out that graph data with large sensitive homophily coefficient may enhance bias inGNNs,
the fundamental understanding for message passing and sensitive homophily coefficient is still missing. We provide the theoretical analysis in Section .
